Fine-Mapping Targets and Resolution

What Fine-Mapping Is Trying to Resolve

A genomic region can show convincing evidence of association with a trait while leaving an important question unanswered: which variant or variants in the region are responsible for the signal? Fine-mapping addresses this variant-level localisation problem. Its target is not simply to confirm that some association exists, nor to estimate a trait effect as precisely as possible. It is to evaluate uncertainty about which candidate variants are causal, conditional on a region under analysis and a specified statistical model.

This distinction matters because many variants can have similar-looking association evidence. A regional association result may make the presence of a signal plausible, but it does not by itself identify its causal source. Likewise, a precise estimate of an association effect for one measured variant is not automatically a precise identification of the causal variant.

Definition: Let $R$ denote a genomic region chosen for analysis, $D$ the data used in the analysis, and $m$ the number of candidate variants in that region. The fine-mapping target is the model-based uncertainty about which of those $m$ candidates, if any, are causal, conditional on $D$, $R$, and the assumptions of the model. Resolution describes how concentrated that uncertainty is on particular variants or small groups of variants; it is not the same as the strength of evidence that the region is associated.

The word “causal” here is statistical and conditional on the model. A variant assigned high causal probability by a fine-mapping analysis is not thereby proved to act through a particular molecular mechanism. The interpretation also depends on adequate variant coverage, correct allele and genotype data, an appropriate model for the trait, and a suitable representation of dependencies among variants. If those conditions fail, a sharply concentrated result can still be misleading.

Three Questions That Must Not Be Confused

It is useful to separate three inferential questions. Association detection asks whether the data provide evidence against a no-association null hypothesis for a marker or region. Fine-mapping asks how uncertainty about causal status is distributed among candidate variants. Effect estimation asks about the magnitude and direction of an effect under a specified model. The questions are related, but no one of them answers the others automatically.

Task	Typical question	What the result does not establish by itself
Association detection	Is there evidence that the trait is associated with a marker or region?	Which variant is causal, or what biological mechanism operates
Fine-mapping	How uncertain are we about the causal candidate variant or variants?	That the region is causal for the trait under every model, or that an effect estimate is unbiased
Effect estimation	How large is an estimated trait change per allele, under a stated model?	That the measured variant is the causal source of the signal

Fine-mapping is usually conducted after a region has been selected because it shows evidence of association. That conditioning defines the practical target, but it does not erase the selection process. A reported result should make clear which region and variants were considered, what data and model were used, and whether the analysis allows one or multiple causal variants. Regional selection, incomplete coverage, or a misspecified model can affect the resulting variant-level uncertainty.

Worked Example: A Strong Regional Signal With Residual Variant Uncertainty

Suppose a hypothetical analysis considers three candidate variants in a region already selected for follow-up. Under a model allowing at most one causal candidate, the reported posterior probabilities are $P(C=0\mid D,R)=0.08$, $P(C=1\mid D,R)=0.62$, $P(C=2\mid D,R)=0.25$, and $P(C=3\mid D,R)=0.05$. Here $C=0$ means no candidate is causal and $C=j$ means candidate $j$ is causal.

The probabilities sum to one: $0.08+0.62+0.25+0.05=1.00$. The probability that at least one candidate is causal is therefore $1-0.08=0.92$. Conditional on at least one being causal, the probability assigned to candidate 1 is

P(C=1\mid D,R,C\ne 0)=\frac{0.62}{0.92}=0.6739.

Thus candidate 1 has the largest probability, but it accounts for about 67.4% of the posterior probability conditional on a non-null candidate. The remaining probability is distributed between candidates 2 and 3. The result supports prioritising candidate 1, but it does not justify saying that candidate 1 has been identified with certainty. This calculation concerns localisation; it is not an association test or an estimate of the trait effect.

Configurations and the Probability of Any Causal Candidate

When a model allows more than one causal variant, it is important to represent the candidate status as a configuration rather than as one mutually exclusive label. Let $S$ be the subset of candidate indices that are causal. For example, $S=\{1,3\}$ means candidates 1 and 3 are causal, while $S=\varnothing$ means none of the candidates is causal. The configurations are mutually exclusive and collectively exhaustive within the model.

Definition: In a model allowing multiple causal candidates, the probability that the region contains at least one causal candidate is $$ P(A\mid D,R)=\sum_{S\ne\varnothing}P(S\mid D,R), \qquad A=\{S\ne\varnothing\}, $$ where the sum is over all nonempty configurations permitted by the model. The marginal probability that candidate $j$ is causal is $$ P(j\in S\mid D,R)=\sum_{S:\,j\in S}P(S\mid D,R). $$

In a model allowing at most one causal candidate, the permitted configurations are $\varnothing,\{1\},\ldots,\{m\}$. Writing $C=0$ for $\varnothing$ and $C=j$ for $\{j\}$, the events $C=1,\ldots,C=m$ are mutually exclusive. Consequently, in this restricted model,

P(A\mid D,R)=\sum_{j=1}^{m}P(C=j\mid D,R)=1-P(C=0\mid D,R).

The restriction is essential. If configurations can contain multiple candidates, summing the marginal probabilities that each candidate is causal can count a configuration more than once. A short way to see the distinction is to use indicator variables: the number of causal candidates is $|S|=\sum_{j=1}^{m} I(j\in S)$. Taking conditional expectations gives

E(|S|\mid D,R)=\sum_{j=1}^{m}P(j\in S\mid D,R).

This is an expected number of causal candidates, not the probability of at least one. The latter is the sum over nonempty configurations, each counted once.

Worked Example: Multiple Causal Variants and Double-Counting

Consider three candidates and a hypothetical model that assigns the following posterior probabilities to configurations: $P(S=\varnothing\mid D,R)=0.05$, $P(S=\{1\}\mid D,R)=0.20$, $P(S=\{2\}\mid D,R)=0.15$, $P(S=\{1,2\}\mid D,R)=0.45$, and $P(S=\{3\}\mid D,R)=0.15$. These probabilities sum to $1.00$.

The probability of at least one causal candidate is the sum of the probabilities of the four nonempty configurations:

P(A\mid D,R)=0.20+0.15+0.45+0.15=0.95.

The marginal probability for candidate 1 is $0.20+0.45=0.65$, because candidate 1 appears in configurations $\{1\}$ and $\{1,2\}$. For candidate 2 it is $0.15+0.45=0.60$, and for candidate 3 it is $0.15$. Their sum is $0.65+0.60+0.15=1.40$, which is not the probability that any candidate is causal. It is the expected number of causal candidates:

E(|S|\mid D,R)=1(0.20)+1(0.15)+2(0.45)+1(0.15)=1.40.

The configuration $\{1,2\}$ contributes probability $0.45$ once to the event “at least one is causal,” but contributes to both candidate 1’s and candidate 2’s marginal probabilities. This is why the two summaries answer different questions.

Resolution Is About Localisation, Not Just Significance

A fine-mapping result has high resolution when its uncertainty is concentrated on a small number of candidates, subject to the model and data. If probability is spread across many variants, the region may still have strong association evidence while variant-level resolution remains limited. Conversely, a result that concentrates probability on one candidate is not automatically reliable: concentration can arise from model assumptions, omitted variants, or data problems as well as genuine information in the data.

A posterior probability for a candidate is a model-based probability of its causal status conditional on the specified data, region, and model. It is not the probability that the association test is significant, and it is not a probability that a particular biological mechanism is true. When a model allows multiple causal variants, candidate-level marginal probabilities can overlap because several candidates may be causal together.

Worked Example: Detection, Effect Size, and Localisation Give Different Answers

Suppose a hypothetical study reports an estimated association coefficient of $0.18$ trait units per additional effect allele for a marker, with standard error $0.03$ trait units per allele. Under a large-sample normal approximation for the coefficient, the Wald statistic for testing $H_0:\beta=0$ is

z=\frac{0.18}{0.03}=6.00.

A two-sided standard normal test gives $P(|Z|\ge 6.00)\approx 1.97\times10^{-9}$, which is strong evidence against the no-association null for that marker under the test assumptions. The coefficient estimates an association difference of $0.18$ trait units per additional effect allele; it does not, by itself, prove that the marker is causal.

Now suppose a separate hypothetical fine-mapping model for the region assigns conditional probabilities $0.52$, $0.41$, and $0.07$ to three candidates under a single-causal-candidate assumption. These probabilities sum to $1.00$, but the leading candidate has only $0.52$ of the probability. The association result is strong, the estimated coefficient has a stated magnitude and unit, and the candidate localisation remains uncertain. Each statement is valid, but each describes a different inferential target.

The normal approximation and standard error must be appropriate for the coefficient test, and the fine-mapping probabilities must come from a model whose variant coverage and assumptions are defensible. Without those conditions, neither the small p-value nor the probability ranking should be treated as a guarantee of correctness.

Assumptions, Diagnostics, and Failure Modes

Fine-mapping conclusions depend on the candidate set and model being adequate. At minimum, interpretation requires that the variants under consideration are represented correctly, allele labels are harmonised, and the phenotype and genotype analyses are sufficiently well specified. The analysis must also account appropriately for the dependence among variants in the region. If a true causal variant is absent from the candidate set, probability assigned to listed variants can be distorted; the method cannot select a variant it was not allowed to consider.

Useful checks focus on whether the result is stable and whether the inputs support the intended interpretation. Review the region definition and variant list; verify allele alignment and quality control; check that the data and model use compatible effect-allele conventions; and compare the stated model’s assumptions with the scientific setting. Where results change substantially under reasonable changes in model assumptions or candidate coverage, report that sensitivity rather than presenting a single ranking as definitive.

Over-reading a small p-value: a small association p-value can support detection, but does not show that one particular candidate is causal.
Calling the top-ranked variant “the causal variant” without qualification: a ranking gives an ordering under a model; substantial probability may remain elsewhere.
Ignoring the null configuration: if the model includes the possibility that no candidate is causal, state whether reported candidate probabilities are unconditional or conditional on at least one being causal.
Adding marginal probabilities in a multiple-candidate model: this gives an expected count, not the probability that any candidate is causal. Sum probabilities over nonempty configurations for the latter.
Confusing an association coefficient with a causal effect: a coefficient is tied to its statistical model and measured marker; causal interpretation requires additional assumptions.

Choosing the Appropriate Claim

Association testing, effect estimation, and fine-mapping are complementary rather than competing procedures. An association test is appropriate for asking whether a signal is present under its null model. Effect estimation is appropriate for quantifying an estimated trait difference and its uncertainty. Fine-mapping is appropriate for allocating uncertainty among candidate causal variants, conditional on a specified region and model. Functional evidence can help interpret candidates, but it does not replace a clear statement of what the statistical analysis estimated.

The appropriate resolution claim should match the result. A broad distribution of candidate probabilities supports prioritisation of a region or group of variants, not a unique causal-variant claim. A concentrated distribution supports a more specific model-based prioritisation, but remains conditional on data quality, candidate coverage, and assumptions. Even a well-resolved variant-level result does not by itself identify the biological pathway or establish that changing the variant would produce the estimated trait difference.

Key takeaway: Fine-mapping concerns uncertainty about causal variant identity within a specified region. Keep that target separate from detecting association and estimating effect size, and define carefully whether the model allows one or multiple causal variants.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

A region contains four candidates. A model allows at most one causal candidate and assigns probability $0.10$ to the null configuration. What is the probability that at least one candidate is causal?
In a multiple-candidate model, the probabilities of the nonempty configurations are $0.30$ for $\{1\}$, $0.25$ for $\{2\}$, and $0.35$ for $\{1,2\}$. What is the probability of at least one causal candidate, and what are the marginal probabilities for candidates 1 and 2?
A marker has a very small association p-value, but a fine-mapping model distributes probability nearly equally over ten candidates. What can be concluded about detection and localisation?
A coefficient is estimated as $0.40$ trait units per allele with standard error $0.10$. Does this alone establish that the marker is causal? State what the coefficient describes and why the causal claim does not follow.

Solutions. (1) The probability of at least one causal candidate is $1-0.10=0.90$, because the single-candidate configurations and the null configuration exhaust the model. (2) The nonempty configuration probabilities sum to $0.30+0.25+0.35=0.90$. Candidate 1 has marginal probability $0.30+0.35=0.65$, and candidate 2 has marginal probability $0.25+0.35=0.60$. Their sum, $1.25$, is an expected count, not the probability of any causal candidate. (3) The small p-value supports association detection under its test assumptions, while the spread across candidates indicates limited variant-level localisation; it does not identify one causal candidate. (4) The coefficient describes an estimated association difference of $0.40$ trait units per additional allele under the fitted model. Its value and standard error alone do not establish causal status; that requires appropriate causal assumptions and a separate assessment of variant-level uncertainty.